$A$ uniform non-deformable cylinder of mass $m$ and radius $R$ is rolling without slipping on a horizontal rough surface. The force of friction is

$A$ particle on the outer surface of a wheel,which is initially at rest,is in contact with the ground at point $P$. Find the displacement of this particle when the wheel completes half a rotation in the forward direction. (Radius of the wheel $= 5 \ m$)

$A$ circular disc of mass $2 \,kg$ and radius $10 \,cm$ rolls without slipping with a speed $2 \,m/s$. The total kinetic energy of the disc is .......... $J$.

$A$ solid sphere is in rolling motion. In rolling motion,a body possesses translational kinetic energy $(K_t)$ as well as rotational kinetic energy $(K_r)$ simultaneously. The ratio $K_t : (K_t + K_r)$ for the sphere is

$A$ ring and a disc roll on a horizontal surface without slipping with the same linear velocity. If both have the same mass and the total kinetic energy of the ring is $6 \ J$,then the total kinetic energy of the disc is: (in $/2 \ J$)

$A$ solid sphere of mass $500 \ g$ and radius $10 \ cm$ rolls without slipping with a velocity of $20 \ cm/s$. The total kinetic energy of the sphere will be ........ $J$.